A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes

TL;DR

This paper introduces a Lagrangian finite element method for modeling thermo-electromagnetic problems in deforming cylindrical geometries, aiming to facilitate simulations of electrically assisted forming processes without remeshing.

Contribution

It presents a novel Lagrangian approach for solving time-varying thermo-electromagnetic problems, avoiding remeshing and enabling efficient simulation of deforming geometries.

Findings

Validated numerical implementation in FEniCS.

Accurate modeling of temperature and power dissipation in deforming cylinders.

Potential application to electromechanical forming processes.

Abstract

The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermoelectromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an inplane current; the source will be given in terms of currents or voltages defined at sorne parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.